Low-loss tunable radio frequency filter

ABSTRACT

A method of constructing an RF filter comprises designing an RF filter that includes a plurality of resonant elements disposed, a plurality of non-resonant elements coupling the resonant elements together to form a stop band having a plurality of transmission zeroes corresponding to respective frequencies of the resonant elements, and a sub-band between the transmission zeroes. The non-resonant elements comprise a variable non-resonant element for selectively introducing a reflection zero within the stop band to create a pass band in the sub-band. The method further comprises changing the order in which the resonant elements are disposed along the signal transmission path to create a plurality of filter solutions, computing a performance parameter for each of the filter solutions, comparing the performance parameters to each other, selecting one of the filter solutions based on the comparison of the computed performance parameters, and constructing the RF filter using the selected filter solution.

RELATED APPLICATIONS DATA

This application is a continuation of U.S. patent application Ser. No.14/214,249, filed Mar. 14, 2014, now issued as U.S. Pat. No. 8,922,294,which is a continuation-in-part of U.S. patent application Ser. No.13/282,289, filed Oct. 26, 2011, now issued as U.S. Pat. No. 8,797,120,which is a continuation of U.S. patent application Ser. No. 12/959,237,filed Dec. 2, 2010, now issued as U.S. Pat. No. 8,063,714, which is acontinuation of U.S. patent application Ser. No. 12/620,455, filed Nov.17, 2009, now issued as U.S. Pat. No. 7,863,999, which is a continuationof U.S. patent application Ser. No. 12/163,814, filed Jun. 27, 2008, nowissued as U.S. Pat. No. 7,639,101, which claims priority from U.S.Provisional Patent Application Ser. No. 60/937,462, filed Jun. 27, 2007,and is a continuation-in-part of U.S. patent application Ser. No.11/561,333, filed Nov. 17, 2006, now issued as U.S. Pat. No. 7,719,382,which applications are all incorporated herein by reference.

FIELD OF THE INVENTION

The present inventions generally relate to microwave circuits, and inparticular, microwave band-pass filters.

BACKGROUND OF THE INVENTION

Electrical filters have long been used in the processing of electricalsignals. In particular, such electrical filters are used to selectdesired electrical signal frequencies from an input signal by passingthe desired signal frequencies, while blocking or attenuating otherundesirable electrical signal frequencies. Filters may be classified insome general categories that include low-pass filters, high-passfilters, band-pass filters, and band-stop filters, indicative of thetype of frequencies that are selectively passed by the filter. Further,filters can be classified by type, such as Butterworth, Chebyshev,Inverse Chebyshev, and Elliptic, indicative of the type of bandshapefrequency response (frequency cutoff characteristics) the filterprovides relative to the ideal frequency response.

The type of filter used often depends upon the intended use. Incommunications applications, band-pass filters are conventionally usedin cellular base stations and other telecommunications equipment tofilter out or block RF signals in all but one or more predefined bands.For example, such filters are typically used in a receiver front-end tofilter out noise and other unwanted signals that would harm componentsof the receiver in the base station or telecommunications equipment.Placing a sharply defined band-pass filter directly at the receiverantenna input will often eliminate various adverse effects resultingfrom strong interfering signals at frequencies near the desired signalfrequency. Because of the location of the filter at the receiver antennainput, the insertion loss must be very low so as to not degrade thenoise figure. In most filter technologies, achieving a low insertionloss requires a corresponding compromise in filter steepness orselectivity.

In commercial telecommunications applications, it is often desirable tofilter out the smallest possible pass band using narrow-band filters toenable a fixed frequency spectrum to be divided into the largestpossible number of frequency bands, thereby increasing the actual numberof users capable of being fit in the fixed spectrum. With the dramaticrise in wireless communications, such filtering should provide highdegrees of both selectivity (the ability to distinguish between signalsseparated by small frequency differences) and sensitivity (the abilityto receive weak signals) in an increasingly hostile frequency spectrum.Of most particular importance is the frequency ranges of 800-900 MHzrange for analog cellular communications, and 1,800-2,200 MHz range forpersonal communication services (PCS).

Of particular interest to the present invention is the need for ahigh-quality factor Q (i.e., measure of the ability to store energy, andthus inversely related to its power dissipation or lossiness), lowinsertion loss, tunable filter in a wide range of microwave and RFapplications, in both military (e.g., RADAR), communications, andelectronic intelligence (ELINT), and the commercial fields, such as invarious communications applications, including cellular. In manyapplications, a receiver filter must be tunable to either select adesired frequency or to trap an interfering signal frequency. Thus, theintroduction of a linear, tunable, band-pass filter between the receiverantenna and the first non-linear element (typically a low-noiseamplifier or mixer) in the receiver, offers substantial advantages in awide range of RF microwave systems, providing that the insertion loss isvery low.

For example, in commercial applications, the 1,800-2,200 MHz frequencyrange used by PCS can be divided into several narrower frequency bands(A-F bands), only a subset of which can be used by a telecommunicationsoperator in any given area. Thus, it would be beneficial for basestations and hand-held units to be capable of being reconfigured tooperate with any selected subset of these frequency bands. As anotherexample, in RADAR systems, high amplitude interfering signals, eitherfrom “friendly” nearby sources, or from jammers, can desensitizereceivers or intermodulate with high-amplitude clutter signal levels togive false target indications. Thus, in high-density signalenvironments, RADAR warning systems frequently become completelyunusable, in which case, frequency hopping would be useful.

Microwave filters are generally built using two circuit building blocks:a plurality of resonators, which store energy very efficiently at onefrequency, f₀; and couplings, which couple electromagnetic energybetween the resonators to form multiple stages or poles. For example, afour-pole filter may include four resonators. The strength of a givencoupling is determined by its reactance (i.e., inductance and/orcapacitance). The relative strengths of the couplings determine thefilter shape, and the topology of the couplings determines whether thefilter performs a band-pass or a band-stop function. The resonantfrequency f₀ is largely determined by the inductance and capacitance ofthe respective resonator. For conventional filter designs, the frequencyat which the filter is active is determined by the resonant frequenciesof the resonators that make up the filter. Each resonator must have verylow internal resistance to enable the response of the filter to be sharpand highly selective for the reasons discussed above. This requirementfor low resistance tends to drive the size and cost of the resonatorsfor a given technology.

Typically, fixed frequency filters are designed to minimize the numberof resonators required to achieve a certain shape as the size and costof a conventional filter will increase linearly with the number ofresonators required to realize it. As is the case for semiconductordevices, photolithographically defined filter structures (such as thosein high-temperature superconductor (HTS), micro electro-mechanicalsystems (MEMS), and film bulk acoustic resonator (FBAR) filters are muchless sensitive to this kind of size and cost scaling than conventionalcombline or dielectric filters.

The approaches used to design tunable filters today follow the sameapproach as described above with respect to fixed frequency filters.Thus, they lead to very efficient, effective, and simple circuits; i.e.,they lead to the simplest circuit necessary to realize a given filterresponse. In prior art tuning techniques, all the resonant frequenciesof the filter are adjusted to tune the filter's frequency. For example,if it is desired to increase the operating frequency band of the deviceby 50 MHz, all of the resonant frequencies of the narrow-band filtermust be increased by 50 MHz. While this prior art technique has beengenerally successful in adjusting the frequency band, it inevitablyintroduces resistance into the resonators, thereby disadvantageouslyincreasing the insertion loss of the filter.

Although HTS filters may be tuned without introducing significantresistance into the resonators by mechanically moving an HTS plate aboveeach resonator in the filter to change its resonant frequency, suchtechnique is inherently slow (on the order of seconds) and requiresrelative large three-dimensional tuning structures. Insertion loss canbe reduced in so-called switched filter designs; however, these designsstill introduce a substantial amount of loss between switching times andrequire additional resonators. For example, the insertion-loss of afilter system can be reduced, by providing two filters and a pair ofsingle-pole double-throw (SP2T) switches to select between the filters,thus effectively reducing the tuning range requirement, but increasingthe number of resonators by a factor of two and introducing loss fromthe switch. The loss of the filter system can further be reduced byintroducing more switches and filters, but each additional filter willrequire the same number of resonators as the original filter and willintroduce more loss from the required switches.

There, thus, remains a need to provide a band-pass filter that can betuned quickly with a decreased insertion loss.

SUMMARY OF THE INVENTION

In accordance with the present inventions, a method of constructing aradio frequency (RF) filter is provided. The RF filter comprises asignal transmission path having an input and an output, a plurality ofresonant elements (e.g., acoustic resonators) disposed along the signaltransmission path between the input and the output, and a plurality ofnon-resonant elements coupling the resonant elements together. Theresonant elements are coupled together to form a stop band having aplurality of transmission zeroes corresponding to respective frequenciesof the resonant elements, and at least one sub-band between thetransmission zeroes. The non-resonant elements have susceptance valuesthat locate at least one reflection zero within the stop band to createa pass band in one of the at least one sub-bands.

The non-resonant elements comprise at least one non-resonant element forthat introduces at least one reflection zero within the stop band tocreate a pass band in one of the sub-band(s). In one embodiment, thenon-resonant element(s) are variable non-resonant element(s) forselectively introducing the reflection zero(es) within the stop band tocreate the pass band in the one sub-band. In one embodiment, a pluralityof sub-bands is provided, in which case, the variable non-resonantelement(s) may be for displacing the reflection zero(es) along the stopband to create the pass band within selected ones of the sub-bands. Thepass band may have substantially different bandwidths within theselected sub-bands. In another embodiment, the variable non-resonantelement(s) is for displacing at least another reflection zero within thestop band to create another pass band within another one of thesub-bands.

The variable non-resonant element may have, e.g., an adjustablesusceptance, and may include one or more of a variable capacitor, aloss-loss switch, a varactor, and a switched capacitor. In oneembodiment, each of the resonant elements comprises a thin-film lumpedelement structure (such as, e.g., a high temperature superconductor(HTS)), although a resonant element can take the form of any structurethat resonates at a desired frequency. The RF filter may optionallyfurther include a controller configured for generating electricalsignals to adjust the variable non-resonant element(s).

The method comprises changing the order in which the resonant elementsare disposed along the signal transmission path to create a plurality offilter solutions, computing a performance parameter (e.g., anintermodulation distortion, insertion loss, or power handling) for eachof the filter solutions, comparing the performance parameters to eachother, selecting one of the filter solutions based on the comparison ofthe computed performance parameters, and constructing the RF filterusing the selected filter solution. One method further comprisesgenerating a coupling matrix representation for each of the filtersolutions, in which case, the performance parameter for each of thefilter solutions may be computed from the respective coupling matrixrepresentation. The filter design may include nodes respectively betweenthe first set of non-resonant elements, nodes respectively between theplurality of resonant elements and the second set of non-resonantelements, and nodes at the input and output, in which case, eachdimension of the coupling matrix includes the nodes. The method mayoptionally further comprise reducing each coupling matrix to itssimplest form, and determining whether the reduced coupling matrices aredifferent relative to each other.

Other and further aspects and features of the invention will be evidentfrom reading the following detailed description of the preferredembodiments, which are intended to illustrate, not limit, the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings illustrate the design and utility of preferred embodimentsof the present invention, in which similar elements are referred to bycommon reference numerals. In order to better appreciate how theabove-recited and other advantages and objects of the present inventionsare obtained, a more particular description of the present inventionsbriefly described above will be rendered by reference to specificembodiments thereof, which are illustrated in the accompanying drawings.Understanding that these drawings depict only typical embodiments of theinvention and are not therefore to be considered limiting of its scope,the invention will be described and explained with additionalspecificity and detail through the use of the accompanying drawings inwhich:

FIG. 1 is a block diagram of a tunable radio frequency (RF) filterconstructed in accordance with one embodiment of the present inventions;

FIG. 2 is a plot of a modeled frequency response of an exemplary widestop band using eight resonant elements;

FIG. 3 is a plot of the frequency response of FIG. 2, wherein a passband has been introduced within a sub-band of the stop band;

FIGS. 4( a)-4(g) are plots of the frequency response of FIG. 2, whereina pass band has been introduced within selected sub-bands of the stopband;

FIGS. 5( a)-5(d) are plots of the frequency response of FIG. 2, whereinthe stop band has been shifted in frequency and a pass band has beenintroduced at various locations of a sub-band of the shifted stop band;

FIG. 6 is a plot illustrating the simultaneous shifting of transmissionzeroes of the frequency response of FIG. 2 to extend the range of thepass band introduced within the selected sub-bands of the stop band ofFIGS. 4( a)-4(g);

FIGS. 7( a)-7(f) are plots of a modeled frequency response of anexemplary wide stop band using nine resonant elements, wherein a passband has been introduced within selected sub-bands of the stop band tocover the personal communications services (PCS) frequency range;

FIG. 8 are plots illustrating the independent shifting of transmissionzeroes of the frequency response of FIGS. 7( a)-7(f) to accommodate theintroduction of the pass band within the selected sub-bands of the stopband;

FIGS. 9( a)-9(f) are plots of a modeled frequency response of FIG. 2,wherein multiple pass bands have been introduced within selectedsub-bands of the stop band;

FIG. 10 is a block diagram of a tunable RF filter constructed inaccordance with another embodiment of the present inventions;

FIG. 11 is a plot of a modeled frequency response of the filter of FIG.10, wherein a pass band has been introduced at various locations of thesub-band of the shifted stop band;

FIG. 12 is a plot illustrating the variation of coupling values ofnon-resonant elements used in the tunable RF filter of FIG. 10 versus afrequency shift in the pass-band of FIG. 11;

FIGS. 13( a)-13(d) illustrate circuit representations of the tunable RFfilter of FIG. 1;

FIG. 14 is a table illustrating component values used in modeling the RFfilter of FIG. 14 for three filter states;

FIGS. 15( a)-15(c) is a circuit implementation of the tunable RF filterof FIG. 1, particularly illustrating various filter states andcorresponding frequency responses;

FIGS. 16( a)-16(c) are plots of the frequency response of the RF filterof FIG. 14 in the three states;

FIG. 17 is a plot illustrating the tuning of the RF filter of FIG. 14versus insertion loss of the filter;

FIG. 18 is a plot comparing the insertion loss of the RF filter of FIG.14 versus the insertion loss of a conventional filter when tuned overthe same frequency range;

FIG. 19 is a plot comparing the insertion loss of the filter of FIG. 1versus the insertion loss of a switched filter when tuned over the samefrequency range;

FIG. 20 is a plot comparing frequency responses between two-resonator,four-resonator, and six-resonator tunable filters constructed inaccordance with the present inventions and a frequency response of astandard band-pass filter;

FIG. 21 illustrates another circuit representation of the tunable RFfilter of FIG. 1;

FIG. 22 illustrates a coupling matrix of the circuit representation ofFIG. 21;

FIGS. 23( a)-23(c) are plots of the frequency responses of the RF filterof FIG. 21 and corresponding coupling matrices;

FIG. 24 is a plot graphically showing the coupling values in thecoupling matrices of FIGS. 23( a)-23(c) used to tune the RF filter ofFIG. 21;

FIG. 25 is a plot graphically showing another set of coupling valuesthat can be used to tune the RF filter of FIG. 21;

FIG. 26 is a plot graphically showing still another set of couplingvalues that can be used to tune the RF filter of FIG. 21;

FIG. 27 is a plan view layout of one resonator of the tunable RF filterof FIG. 1, particularly illustrating tuning forks for tuning theresonator;

FIG. 28 is a plan view layout of one resonator of the tunable RF filterof FIG. 1, particularly illustrating trimming tabs for tuning theresonator; and

FIG. 29 is a block diagram of another tunable RF filter constructed inaccordance with one embodiment of the present inventions.

DETAILED DESCRIPTION OF THE EMBODIMENTS

Referring to FIG. 1, a tunable radio frequency (RF) filter 10constructed in accordance with the present inventions will now bedescribed. In the illustrated embodiment, the RF filter 10 is aband-pass filter having pass band tunable within a desired frequencyrange, e.g., 800-900 MHz or 1,800-2,220 MHz. In a typical scenario, theRF filter 10 is placed within the front-end of a receiver (not shown)behind a wide pass band filter that rejects the energy outside of thedesired frequency range. The RF filter 10 generally comprises a signaltransmission path 12 having an input 14 and an output 16, a plurality ofnodes 17 disposed along the signal transmission path 12, a plurality ofresonant branches 19 respectively extending from the nodes 17, and aplurality of non-resonant branches 21 respectively extending from thenodes 17. The RF filter 10 further comprises a plurality of resonantelements 18 (in this case, four) between the input 14 and output 16, andin particular coupled between the resonant branches 21 and ground, aplurality of tuning elements 20 for adjusting the frequencies of theresonant elements 18, a plurality of non-resonant elements 22 couplingthe resonant elements 18 together, four of which are coupled between thenon-resonant branches 21 and ground. The RF filter 10 further comprisesan electrical controller 24 configured for tuning the RF filter 10 to aselected narrow-band within the frequency range.

The signal transmission path 12 may comprise a physical transmissionline to which the non-resonant elements 22 are directly or indirectlycoupled to, although in alternative embodiments, a physical transmissionline is not used. In the illustrated embodiment, the resonant elements18 includes lumped element electrical components, such as inductors andcapacitors, and in particular, thin-film lumped structures, such asplanar spiral structures, zig-zag serpentine structures, single coilstructures, and double coil structures. Such structures may include thinfilm epitaxial high temperature superconductors (HTS) that are patternedto form capacitors and inductors on a low loss substrate. Furtherdetails discussing high temperature superconductor lumped elementfilters are set forth in U.S. Pat. No. 5,616,539, which is expresslyincorporated herein by reference.

In the illustrated embodiment, the resonant elements 18 are representedby susceptance B^(R), and the non-resonant elements 22 are representedby susceptance B^(N), which are coupled in parallel with the resonantelements 18, and admittance inverters J, which are coupled between theresonant elements 18. Selected ones of the non-resonant elements 22 canbe varied, while any remaining ones of the non-resonant elements 22remained fixed.

As will be described in greater detail below, the non-resonant elements22 may be varied to tune the pass band substantially over the entirefrequency range, with the frequencies of the resonant elements 18, ifnecessary, only slightly adjusted to accommodate and/or move the passband within a relatively portion of the frequency range. In this manner,the insertion loss of the filter 10 is significantly reduced, since itis the non-resonant elements 22, rather than the resonant elements 18,that are used as the primary means for tuning the filter 10. That is,because adjustment of the non-resonant elements 22 contributes less tothe loss of the filter 10 than does the adjustment of the significantlyloss sensitive resonant elements 18, the filter 10 will have less lossthan prior art filters that utilize resonant elements as the main meansfor tuning the filter 10. In addition, since the frequencies of theresonant elements 18 are adjusted very little, if at all, the tuningspeed of the filter 10 is increased.

The RF filter 10 accomplishes the foregoing by introducing a narrow passband with selected regions of a wide stop band. That is, although the RFfilter 10 is ultimately used as a pass band filter, the resonantelements 18 are actually coupled together by the non-resonant elements22—not to create a pass band, but rather to create a wide stop bandresponse having transmission zeroes (in this case, numbering four)corresponding to the respective frequencies of the resonant elements 18.The electrical controller 24 then adjusts the non-resonant elements 22to introduce and displace reflection zeroes along the stop band to movea narrow pass band within the desired frequency range. The electricalcontroller 24 may also adjust the frequencies of the resonating elements18 via the tuning elements 20 to move the transmission zeroes along thefrequency range to optimize the filter response. In the illustratedembodiment, the electrical controller 24 including memory (not shown)for storing the values of the non-resonant elements 22 necessary toeffect the desired location of the pass band within the frequency range.

This technique will now be described with reference to various exemplaryfilter responses modeled in accordance with the following equations:

${{S_{11}(s)} = \frac{F(s)}{E(s)}},{{S_{21}(s)} = \frac{P(s)}{ɛ\;{E(s)}}},{{E}^{2} = {{F}^{2} + \frac{{P}^{2}}{ɛ^{2}}}},$where S₁₁ is the input reflection coefficient of the filter, S₂₁ is theforward transmission coefficient, s is the normalized frequency, F and Pare N-order polynomial (where N is the number of resonant elements) ofthe generalized complex frequency s, and ∈ is a constant that definesequal ripple return loss. Each of the coefficients S₁₁ and S₂₁ iscapable of having up to an N number of zero-points, since the numeratorhas an Nth order. When both of the coefficients S₁₁, S₂₁ have all Nzero-points, the filter response is considered fully elliptic. Furtherdetails discussing the modeling of filters are set forth in “MicrostripFilters for RF/Microwave Application,” Jia-Shen G. Hong and M. J.Lancaster, Wiley-Interscience 2001. The normalized frequency, s=iw canbe mapped into real frequency in accordance with the equation:

${w = {\frac{f_{c}}{BW}\left( {\frac{f}{f_{c}} - \frac{fc}{f}} \right)}},$where f is the real frequency, f_(c) is the center frequency, and BW isthe bandwidth of the filter. Further details discussing thetransformation of normalized frequency into real frequency are set forthin “Microwave Filters, Impedance-Matching Networks, and CouplingStructures,” G. Matthaei, L. Young and E. M. T. Jones, McGraw-Hill(1964).

FIG. 2 illustrates an exemplary wide band stop filter response, whichwas modeled using eight resonant elements, thereby creating eightcorresponding transmission zeroes 30 (only six shown) at the respectiveresonant element frequencies (as best shown in the right side view ofFIG. 2) to form a stop band 32, and eight reflection zeroes 34 (only sixshown) that fall outside of this stop band 32 (as best shown in the leftside view of FIG. 2). In this particular example, the transmissionzeroes 30 are positioned at −1.05, −0.75, −0.45, −0.15, 0.15, 0.45,0.75, and 1.05 in the normalized frequency range, thereby creating astop band having a normalized frequency range between −1.05 and 1.05. Asshown in right side view of FIG. 2, the filter response includes seven“bounce-backs” in regions 36 between the transmission zeroes 30 that arerespectively located at −0.90, −0.60, −0.30, 0.0, 0.30, 0.60, and 0.90.Thus, in general, a stop band filter includes an N number oftransmission zeroes (corresponding to the N number of resonantelements), up to N number of reflection zeroes, and an N−1 number ofbounce-back regions 36.

Significantly, a pass band can be formed from any one of thebounce-backs in regions 36 illustrated in FIG. 2 (herein after referredto as “sub-bands”) by displacing at least one of the reflection zeroes34 into the stop band 32 (i.e., by adjusting the values of thenon-resonant elements). For example, FIG. 3 illustrates an exemplaryfilter response where four of the reflection zeroes 34 have beenintroduced into the stop band of FIG. 2 to create a pass band 38 withinthe center sub-band 36(4) (i.e., at 0). The reflection zeroes 34 can bedisplaced along the stop band 32 (i.e., by adjusting the values of thenon-resonant elements), thereby creating the pass band 38 withinselected ones of the sub-bands 36. That is, the reflection zeroes 34 canbe displaced along the stop band 32 to “hop” the pass band 38 betweensub-bands 36.

For example, FIGS. 4( a)-4(g) illustrate exemplary filter responseswhere the four reflection zeroes 34 have been displaced within the stopband 32 to selectively create the pass band 38 in the centers of allseven of the sub-bands 36. That is, going sequentially through FIGS. 4(a)-4(g), the pass band 38 hops from the first sub-band 36(1) (FIG. 4(a)), to the second sub-band 36(2) (FIG. 4( b)), to the third sub-band36(3) (FIG. 4( c)), to the fourth sub-band 36(4) (FIG. 4( d)), to thefifth sub-band 36(5) (FIG. 4( e)), to the sixth sub-band 36(6) (FIG. 4(f)), and then finally to the seventh sub-band 36(7) (FIG. 4( g)). Thus,in the illustrated embodiment, the center of the pass band 38 can hopbetween −0.90, −0.60, −0.30, 0.0, 0.30, 0.60, and 0.90. It should benoted that while the sequence of FIGS. 4( a)-4(g) implies that the passband 38 is hopped between adjacent sub-bands 36, the pass band 38 may behopped between non-adjacent sub-bands 36; for example, from the secondsub-band 36(2) to the fifth sub-band 36(5).

While the pass band 38 can be hopped between sub-bands 36 to discretelycover the desired frequency range, the transmission zeroes 30 can besimultaneously moved in concert from their nominal positions (i.e., byadjusting the frequencies of the resonating elements) to displace theentire stop band 32, and thus the pass band 38, within the normalizedfrequency range. Thus, the pass band 38 can be moved from the centers ofthe sub-bands 36 (i.e., −0.90, −0.60, −0.30, 0.0, 0.30, 0.60, and 0.90)to cover the continuum of the desired frequency range. Thus, if all ofthe transmission zeroes 30 can be displaced by +/−0.15 from theirnominal positions (i.e., resonant elements tuned together in a frequencyrange of +/−0.15), each pass band 38 illustrated in FIGS. 4( a)-4(g)would cover 15% of the normalized frequency range from −1.05 to 1.05.

By way of example, if it is desired to center the pass band 38 at −0.20,the pass band 38 can be located in the third sub-band 36(3) (centered at−0.30 in FIG. 4( c)), and the transmission zeroes 30 can be displaced0.10 from their nominal positions to move the pass band 38 from −0.30 to−0.20. If it is desired to center the pass band 38 at 0.85, the passband 38 can be located in the seventh sub-band 36(7) (centered at 0.90in FIG. 4( g)), and the transmission zeroes 30 can be displaced −0.05from their nominal positions to move the pass band 38 from 0.90 to 0.85.

While the pass band 38 is illustrated in FIGS. 4( a)-4(g) as beingcentered within the sub-bands 36, the reflection zeroes 34 can bedisplaced within the stop band 32 (i.e., by adjusting the values of thenon-resonant elements) to selectively move the pass band 38 within aselected sub-band 36. In this case, the pass band 38 can be hoppedbetween sub-bands 36, as well as moved within each sub-band 36, therebydecreasing the amount the transmission zeroes 30 needed to be adjustedfor the pass band 38 to cover the continuum of the desired frequencyrange. For example, FIGS. 5( a)-5(d) illustrate exemplary filterresponses, with respect to the center sub-band 36(4), where all of thetransmission zeroes 30 are displaced 0.05 from their nominal positions(i.e., by increasing the frequencies of the resonant elements 18 by0.05), and the reflection zeroes 34 are incrementally displaced by 0.05(i.e., by adjusting the non-resonant elements 22) from their nominalpositions.

In particular, going sequentially through FIGS. 5( a)-5(d), thetransmission zeroes 30 are displaced 0.05 from their nominal positions,thereby moving the pass band 38 from 0 (FIG. 5( a)) to 0.05 (FIG. 5(b)). Then, after fixing the transmission zeroes 30 in place, thereflection zeroes 34 are incrementally displaced 0.05 from their nominalpositions to move the pass band 38 from the center of the sub-band 36(4)(0.05 in FIG. 5( b)) to a position 0.05 to the right of the center ofthe sub-band 36(4) (0.10 in FIG. 5( c)), and then to a position 0.10 tothe right of the center of the sub-band 36(4) (0.15 in FIG. 5( d)).

While this modality may disrupt the symmetry of the rejection slope ofthe band-pass filter, in this case, it reduces the needed displacementof the transmission zeroes 30, and thus, the tuning range of theresonant elements, from 15% to 5%, to obtain the same tuning range asthe case where the reflection zeroes 34 are not displaced within asub-band 36. As a result, the loss of filter is further reduced.

Notably, while the transmission zeroes 30 may theoretically be displacedwithin the entirety of a sub-band 36, in which case, each pass band 38can cover approximately 15% of the entire stop band 32 without having totune the resonant elements, in reality, the filter loss significantlyincreases as a reflection zero 34 closely approaches a transmission zero30. As such, it is preferable that the transmission zeroes 30 bedisplaced, along with the reflection zeroes 34, to allow the pass band38 to move within the entire frequency range without significant loss.

For example, referring to FIG. 6, the transmission zeroes 30 aredisplaced in a range of +/−0.05 relative to their nominal positions(shown by horizontal dashed lines) to allow the pass band 38 to belocated anywhere within the nominal frequency range of −1.05 to 1.05 (asrepresented by the diagonal dashed line). As the frequency of pass band38 moves from −1.05 to 1.05, the reflection zeroes 34 hop from onesub-band 36 to the next, with the reflection zeroes 34 being displacedalong a sub-band 36 within a range of +/−0.10, and the transmissionzeroes 30 being displaced within range of +/−0.05, for a total range of0.30 between hops.

In particular, at the beginning of the tuning range, the transmissionzeroes 30 will initially be positioned −0.05 relative to their nominalpositions (i.e., −1.05, −0.75, −0.45, −0.15, 0.15, 0.45, 0.75, 1.05),which places the center the first sub-band 36(1) at −0.95, in whichcase, the reflection zeroes 34 will be initially positioned −0.10relative to their nominal positions in the first sub-band 36(1) to placethe pass band 38 at −1.05. While the transmission zeroes 30 are fixed,the reflection zeroes 34 can be displaced to their nominal positions inthe first sub-band 36(1) to move the pass band 38 from −1.05 to −0.95.While the reflection zeroes 34 are fixed, the transmission zeroes 30 canthen be displaced 0.05 relative to their nominal positions, which movesthe center of the first sub-band 36(1) to −0.85, thereby moving the passband from −0.95 to −0.85. While the transmission zeroes 30 are againfixed, the reflection zeroes 34 can be displaced 0.10 relative to theirnominal positions to move the pass band 38 from −0.85 to −0.75.

Once the pass band 38 reaches −0.75, the reflection zeroes 34 will thenhop from the first sub-band 36(1) to the second sub-band 36(2), and thetransmission zeroes 30 will then again be displaced −0.05 relative totheir nominal positions, which moves the center of the second sub-band36(2) to −0.65, in which case, the reflection zeroes 34 will beinitially positioned −0.10 relative to their nominal positions tomaintain the pass band 38 at −0.75. The transmission zeroes 30 andreflection zeroes 34 are then moved in coordination with each other inthe same manner described above with respect to the first sub-band 36(1)to move the pass band 38 from −0.75 to −0.45. Once the pass band 38reaches −0.45, the reflection zeroes 34 will then hop from the secondsub-band 36(2) to the third sub-band 36(3), and so forth, until the passband 38 reaches 1.05.

While the RF filter 10 has been described above as being capable oftuning a narrow pass band within a continuum of the desired frequencyrange (i.e., the RF filter 10 can be reconfigured in a continuousmanner), the RF filter 10 may be reconfigurable in a discrete manner,such that the pass band 38 can be discretely centered at selectedregions of the frequency band. For example, in PCS applications, the RFfilter 10 may be reconfigured to operate in any of the six A-F frequencybands by locating the narrow pass band at a selected one of thesefrequency bands.

FIGS. 7( a)-7(f) illustrate exemplary filter responses corresponding tosix different reconfigured states of an RF filter. In this case, themodeled filter has nine transmission zeroes 30 (only seven shown) tocreate a stop band 32 with eight sub-bands 36 located between therespective transmission zeroes 30, and seven reflection zeroes 34 thatcan be displaced into the stop band 32 to create a pass band 38 withinselected ones of the six middle sub-bands 36. Thus, the RF filter can bereconfigured to operate in the A-Band (FIG. 7( a)), D-Band (FIG. 7( b)),B-Band (FIG. 7( c)), E-Band (FIG. 7( d)), F-Band (FIG. 7( e)), or C-Band(FIG. 7( f)) of the PCS communications protocol. As shown, the width ofthe pass band 38 differs within the sub-bands 36, as dictated by theseparation of adjacent transmission zeroes 30. In particular, the widthsof the A-, B-, and C-Bands are approximately two-and-half greater thanthe widths of the D-, E-, and F-Bands.

Notably, because, in this reconfigurable implementation, the pass band38 need not be moved within a continuum of the desired frequency range,but rather is designed to be broad enough to cover the desired frequencyrange, the transmission zeroes 30 are not displaced to extend the rangeof the pass band 38. Rather, as illustrated in FIG. 8, the transmissionzeroes 30 are independently displaced from their nominal positions tomake room for the pass band 38 or otherwise improve rejectionperformance. For example, the second and third transmission zeroes30(2), 30(3) are moved away from each other to make room for thereflection zeroes 34 at the A-Band; the fourth and fifth transmissionzeroes 30(4), 30(5) are moved away from each other to make room for thereflection zeroes at the B-Band, the seventh and eighth transmissionzeroes 30(7), 30(8) are moved away from each other to make room for thereflection zeroes 34 at the C-Band; the third and fourth transmissionzeroes 30(3), 30(4) are moved away from each other to make room for thereflection zeroes 34 at the D-Band, the fifth and sixth transmissionzeroes 30(5), 30 (6) are moved away from each other to make room for thereflection zeroes 34 at the E-Band; and the sixth and seventhtransmission zeroes 30(6), 30(7) are moved away from each other to makeroom for the reflection zeroes 34 at the F-Band.

Although the foregoing techniques have been described as introducing asingle pass band 38 (i.e., one pass band at a time) within the stop band32, multiple pass bands can be introduced within the stop band 32. Forexample, FIGS. 9( a)-9(f) illustrate exemplary filter responses wheretwo sets of four reflection zeroes 34 have been displaced within thestop band 32 to selectively create two pass bands 38(1), 38(2) in thecenters of selected pairs of the sub-bands 36. That is, goingsequentially through FIGS. 9( a)-9(f), the pass bands 38(1), 38(2) areintroduced into the second and third sub-bands 36(2), 36(3) (FIG. 9(a)), into the third and fifth sub-bands 36(3), 36(5) (FIG. 9(b)), intothe third and fourth sub-bands 36(3), 36(4) (FIG. 9( c)), into thesecond and fourth sub-bands 36(2), 36(4) (FIG. 9( d)), into the secondand sixth sub-bands 36(2), 36(6) (FIG. 9( e)), and second and fifthsub-bands 36(2), 36(5) (FIG. 9( f)).

Referring now to FIGS. 10 and 11, a basic tunable filter 50 will bedescribed for the purposes of explaining the correlation between thevalues of variable non-resonant elements (in terms of coupling values)and the movement of a resulting narrow pass band within a wide stopband. As shown in FIG. 10, the RF filter 50 generally comprises a signaltransmission path 52 having an input 54 and an output 56, a plurality ofresonant elements 58 (in this case two) between the input 54 and output56, and a plurality of non-resonant elements 62 coupling the resonantelements 58 together. Tuning elements (not shown) can be used to adjustthe frequencies of the resonant elements 58, and an electricalcontroller (not shown) can be used to tune the RF filter 50 to aselected narrow-band within the frequency range. Like the filter 10illustrated in FIG. 1, the resonant elements 58 of the filter 50 arerepresented by susceptance B^(R), and the non-resonant elements 62 arerepresented by susceptance B^(N), which are coupled in parallel with theresonant elements 58, and admittance inverters J, which are coupledbetween the resonant elements 58. Selected ones of the non-resonantelements 22 can be varied (in this case, the susceptances B^(N)), whileany remaining ones of the non-resonant elements 22 remained fixed (inthis case, the admittance inverters J).

The filter 50 was modeled to create the exemplary filter responseillustrated in FIG. 11. The frequencies of the two resonant elements 58,and thus two transmission zeroes 70, were set at 0.95 GHz and 1.05 GHz,thereby creating a stop band (not shown) having a normalized frequencyrange between 0.95 GHz and 1.05 GHz. In this case, because there areonly two resonant elements 58, a single sub-band 76 is centered betweenthe transmission zeroes 70 at 1.00 GHz. Thus, reflection zeroes (notshown) are introduced and displaced along the stop-band only to move apass-band 78 within the single sub-band 76 (five positions of thepass-band 78 shown)

As further illustrated in FIGS. 11 and 12, the variable non-resonantelements 66 (designated in FIG. 12 as B^(N)(L) and B^(N)(S)) can beadjusted to move the pass band 78 about the nominal frequency of 1.00GHz by changing their coupling values. In particular, the pass band 78will decrease in frequency (move left) as the percentage coupling valueof the load-side non-resonant element B^(N)(L) increases and thepercentage coupling value of the source-side non-resonant elementB^(N)(S) decreases, and will increase in frequency (move right) as thepercentage coupling value of the load-side non-resonant element B^(N)(L)decreases and the percentage coupling value of the source-sidenon-resonant element B^(N)(S) increase.

Referring to FIGS. 13( a)-13(c), the non-resonant elements 22 of thefilter 10 of FIG. 1 can be replaced with actual components, so that thefilter 10 can be modeled and implemented. As shown in FIG. 13( a), thecircuit was first reduced to the constituent components necessary toreconfigure the filter 10 using only the non-resonant elements 22. Inthis case, the tuning elements 20 were not necessary to simulate (model)reconfiguration of the filter 10, and were thus, removed from thecircuit representation in FIG. 13( a). As shown in FIG. 13( b), theblock components of the circuit representation of FIG. 13( a) have beenreplaced with actual circuit components. The non-resonant elements 22represented by B^(N) were replaced with capacitors, the non-resonantelements 22 represented by J were replaced with capacitive pi networks,and the resonant elements 20 represented by B^(R) were replaced withparallel capacitor-inductor combinations. The circuit representation ofFIG. 13( b) was further reduced to the circuit representation of FIG.13( c), the non-resonant elements 22 of which can be varied to effectreconfiguration of the filter 10.

The filter 10 of FIG. 13( c) was emulated using actual circuit componentvalues. The circuit of FIG. 13( c) was modeled in accordance with thepolynomial equations discussed above, with the exception that componentvalues relate to the coefficient of the polynomials. As discussed above,the filter 10 has four resonating elements 18, and therefore, fourtransmission zeroes with three sub-bands formed therebetween, in itsfrequency response. Thus, the values of the capacitors non-resonantelements 22 in the circuit representation of FIG. 13( c) can be adjustedin accordance with one of the three sets of values illustrated in FIG.14 to hop a pass band between the three sub-bands to place the filter 10in a selected one of the three states. Each of the capacitors in thecircuit representation of FIG. 13( c) was modeled in accordance with thecircuit representation of FIG. 13( d). In particular, each capacitor Cwas represented as a circuit having a fixed capacitor C₀ in parallelwith a variable capacitor C_(d), and a resistor R (representing aswitch) in series with the variable capacitor C_(d).

Referring now to FIGS. 15( a)-15(c), the filter 10, using the basicarchitecture illustrated in FIG. 13( c), can be reconfigured between oneof three states by adjusting selected ones of the non-resonant elements22. As shown, all of the frequency responses of the filter 10 have fourtransmission zeroes 30 corresponding to the frequencies of the fourresonant elements 18, and three sub-bands 36 formed between thetransmission zeroes 30. Thus, a pass band 38 can be created in each ofthe three sub-bands 36 to enable a total of three different states: aleft state where the pass band 38 is created in the first sub-band36(1); a middle state where the pass band 38 is created in the secondsub-band 36(2); and a right state where the pass band 38 is created inthe third sub-band 36(3).

As shown, each non-resonant element 22 has three capacitors C₁-C₃ inparallel, with the outer two capacitors C₁ and C₂ having respectiveswitched capacitances in series with resistors R₁ and R₂ stimulatingresistive loss of the switches S₁ and S₂. Thus, the capacitors C₁ and C₂may be included within the circuit by closing the switches S₂ and S₃,and excluded from the circuit by independently opening the switches S₁and S₂. Thus, assuming that capacitors C₁-C₃ have equal values, eachnon-resonant element 22 can have a selected one of the three values: C₁(neither switch S₁, S₂ closed), C₂+C₃ (one of the switches S₁, S₂closed), or C₁+C₂+C₃ (both switches S₁, S₂ closed). The switches S₁ andS₂ can be any suitable loss-switch, such as, e.g., a low-loss GaAsswitch. Alternatively, other variable elements capable of adjusting acapacitance value, such as a variable capacitor, GaAs varactor, orswitch capacitor, can be used.

It has been determined that the pass band 38 can be placed in the firstsub-band 36(1)(left state) when the non-resonant elements 22 have thevalues dictated by the switch states illustrated in FIG. 15( a); in thesecond sub-band 36(2)(middle state) when the non-resonant elements 22have the values dictated by the switch states illustrated in FIG. 15(b); and in the third sub-band 36(3)(middle state) when the non-resonantelements 22 have the values dictated by the switch states illustrated inFIG. 15(c). The filter 10 can be tuned using the parameter extractionand analysis techniques disclosed in U.S. patent application Ser. No.11/289,463, entitled “Systems and Methods for Tuning Filters,” which isexpressly incorporated herein by reference. For purposes ofillustration, light bulbs adjacent switches in closed states have beenshown lit (colored in), and light bulbs adjacent switches in open stateshave been shown unlit (not colored in). While the filter 10 has beendescribed with respect to FIGS. 15( a)-15(c) as only having thecapability of hopping the pass band 38 between sub-bands 36, theresolution of the circuit can be increased by adding more switchedcapacitors in order to enable movement of the pass band 38 within aselected sub-band 36. Also, because the pass band 38 is positioned inthe centers of the sub-bands 36, no tuning elements are shown coupled tothe resonant elements 18.

Referring now to FIG. 17, the emulated filter 10 illustrated in FIG. 13(c) is shown being tuned along the frequency range of 770 MHz to 890 MHzto minimize insertion loss. In this scenario, the filter 10 was tuned byadjusting the non-resonant elements 22 to hop the pass band 38 betweenthe centers of the sub-bands 36 (as illustrated in FIGS. 16( a)-16(c)),and varying the frequencies of the resonant elements 18 to move the passband 38 within the sub-bands 36 (i.e., to cover the frequency rangebetween the centers of the sub-bands 36). As shown, the pass band 38 ismoved from the center of the third sub-band 36(3)(shown in FIG. 15( c))at 890 MHz to the left side of the third sub-band 36(3) at 850 MHz,increasing the insertion loss of the filter 10 from approximately −0.2dB to approximately −1.5 dB. Once it reaches 850 MHz, the pass band 38hops from the third sub-band 36(3) to the center of the second sub-band36(2)(shown in FIG. 15( b)), thereby decreasing the insertion loss fromapproximately −1.5 dB to approximately −0.25 dB. The pass band 38 isthen moved from the center of the second sub-band 36(2) at 850 MHz tothe left side of the second sub-band 36(2) at 810 MHz, increasing theinsertion loss of the filter 10 from approximately −0.25 toapproximately −1.5 dB. Once it reaches 810 MHz, the pass band 38 hopsfrom the second sub-band 36(2) to the center of the first sub-band36(1)(shown in FIG. 15( a)), decreasing the insertion loss fromapproximately −1.5 dB to −0.7 dB. The pass band 38 is then moved fromthe center of the first sub-band 36(1) at 810 MHz to the left side ofthe first sub-band 36(1) at 770 MHz, increasing the insertion loss ofthe filter 10 from approximately −0.7 dB to −1.9 dB. Thus, it can beappreciate that the full range of the frequency range 770 MHz to 890 MHzcan be covered by the filter 10 by moving the pass band 38 along thefrequency range, while hopping between sub-bands 36 to minimizeinsertion loss.

Using the modeled parameters illustrated in FIG. 15, it has beendemonstrated that the insertion loss is significantly decreased across afrequency range when using non-resonant elements 22, as opposed to onlyresonant elements 18, to tune a filter. For example, as shown in FIG.18, the worst case insertion loss of the filter 10 when the non-resonantelements 22 are adjusted, along with the frequencies of the resonantelements 18, to tune the filter 10 over the frequency range 770 MHz to890 MHz is approximately 8 dB less than the insertion loss of the filter10 when only the frequencies of the resonant elements are adjusted totune the filter 10 over the same frequency range.

It has also been demonstrated that the filter 10, as modeled inaccordance with the parameters illustrated in FIG. 15, has an insertionloss that is significantly less than prior art switched filtered tuningtechniques. For example, as shown in FIG. 19, the worst case insertionloss of the filter 10 when the variable non-resonant elements areadjusted, along with the frequencies of the resonant elements, to tunethe filter 10 over the frequency range 770 MHz to 890 MHz issignificantly less than the insertion loss of a switched filter tunedover the same frequency range (assuming small insertion loss from theaddition of a switch and adjusting the frequencies of the resonantelements to cover half of the total tuning range between switching).

Notably, while it has been the conventional thinking that the insertionloss of pass-band filter increases with an increase in the number ofresonant elements, it has been demonstrated that the insertion loss doesnot increase with the number of resonant elements used in a filterutilizing the design techniques described herein. For example, asillustrated in FIG. 20, the frequency response of 2-resonator,4-resonator and 6-resonator filter designs using the techniquesdescribed herein, and a standard filter design, are plotted along thefrequency range from 750 GHz to 950 GHz. As there shown, the Q of theclosest resonant elements—not the number of resonant elements—dominatesthe insertion loss.

It should be noted that varying the values of the non-resonant elements22 that are coupled to the resonant elements 18 in series may slightlyvary the transmission zeroes. It is preferred that these transmissionzeroes not inadvertently move in order to provide the filter with anoptimal performance.

In particular, as shown in FIG. 21, the circuit was again reduced to theconstituent components necessary to reconfigure the filter 10 using onlythe non-resonant elements 22. In this case, the tuning elements 20 werenot necessary to simulate (model) reconfiguration of the filter 10, andwere thus, removed from the circuit representation in FIG. 21.

In the illustrated embodiment, there are four resonant elements 18represented by susceptance B^(R) (in particular, B₁ ^(R), B₂ ^(R), B₃^(R), and B₄ ^(R)) and fifteen non-resonant elements 22, which can bearranged into six non-resonant elements 22(1) (also referred to asNRN-ground (shunt non-resonant element)) represented by susceptanceB^(N) (in particular, B_(S) ^(N), B₁ ^(N), B₂ ^(N), B₃ ^(N), B₄ ^(N) andB_(L) ^(N)), five non-resonant elements 22(2) (also referred to asNRN-NRN (series non-resonant element) represented by admittanceinverters J (in particular, J₀₁, J₁₂, J₂₃, J₃₄, and J₄₅), and fournon-resonant elements 22(3) (also referred to as NRN-resonator(resonator coupling)) represented by admittance inverters J (inparticular, J₁, J₂, J₃, and J₄). The non-resonant elements 22(1), 22(2)are coupled in parallel to the respective resonant elements 18, whilethe non-resonant elements 22(3) are coupled in series to the respectiveresonant elements 18. Selected ones of the non-resonant elements 22 canbe varied, while any remaining ones of the non-resonant elements 22remained fixed. In the illustrated embodiment, the non-resonant elements22 that are coupled in series to the resonant elements 18 (i.e., thenon-resonant elements 22(3)), which tend to “pull” the resonantfrequencies when implemented in a practical solution, remain fixed.

It should be noted that in designs where the resonant elements 18 arerealized using acoustic resonators, such as surface acoustic wave (SAW),film bulk acoustic resonator (FBAR), microelectromechanical system(MEMS) resonators, the non-resonant elements 22 may be realized aseither electrical or mechanical coupling elements. In this case, it maybe advantageous to realize non-resonant elements 22(3) aselectromechanical transducers to allow the non-resonant elements 22(3)and acoustic resonant elements 18 of the circuit to remain fixed, whilestill allowing for electronic tuning using only the non-resonantelements 22(1), 22(2).

FIG. 22 illustrates the coupling matrix representation of the filter 10.As there shown, the nodes S, 1-4, L, and 5-8 (shown in FIG. 20) are onthe left side of the matrix representation, and the nodes S, NRN1-NRN4(non-resonant nodes), L, and resonant nodes R1-R4 are on the top side ofthe matrix representation. As also shown in FIG. 22, the coupling valuesbetween the nodes are the susceptance values and admittance invertervalues of the resonant elements 18 and non-resonant elements 22.

The filter representation illustrated in FIG. 21 was emulated usingdifferent sets of coupling coefficients to hop the pass band 38 betweenthe centers of the sub-bands 36. In particular, FIGS. 23( a)-23(c)illustrate exemplary filter responses (and their corresponding couplingmatrix representation) where four reflection zeroes 34 have beendisplaced within the stop band 32 to selectively create the pass band 38in the centers of all three of the sub-band 36. That is, goingsequentially through FIGS. 23( a)-23(c), the pass band 38 hops from thefirst sub-band 36(1) (FIG. 23( a)), to the second sub-band 36(2) (FIG.23( b)), and then to the third sub-band 36(3) (FIG. 23( c)). Thus, thecenter of the pass band 38 hops between the nominal frequencies −0.80,0.0, and 0.80. As can be appreciated from the corresponding matrixrepresentations shown in FIGS. 23( a)-23(c), the susceptance values forthe serially coupled non-resonant elements 22(3)(i.e., J₁-J₄) are fixedat −1, while the susceptance values and admittance inverter values forthe parallel coupled non-resonant elements 22(1), 22(2) are varied tohop the pass band 38 between the sub-bands 36. The changes (andnon-changes) in these values as the pass band 38 hops between the threenominal frequencies are graphically illustrated in FIG. 24. As thereshown, the values for the parallel coupled non-resonant elements 22(1),(2) (i.e., J₀₁, J₁₂, J₂₃, J₃₄, J₄₅, B₁ ^(N), B₂ ^(N), B₃ ^(N), and B₄^(N)) are varied, whereas the values for the serially couplednon-resonant elements 23(3) (i.e., J₁, J₂, J₃, and J₄) remain constant.

As discussed previously with respect to FIGS. 4( a)-4(g), while the passband 38 can be hopped between sub-bands 36 to discretely cover thedesired frequency range, the transmission zeroes 30 can besimultaneously moved in concert from their nominal positions (i.e., byadjusting the frequencies of the resonating elements) to displace theentire stop band 32, and thus the pass band 38, within the normalizedfrequency range. Thus, with respect to FIGS. 23( a)-23(c), the pass band38 can be moved from the centers of the sub-bands 36 (i.e., −0.80, 0.0,and 0.80) to cover the continuum of the desired frequency range. Thus,if all of the transmission zeroes 30 can be displaced by +/−0.40 fromtheir nominal positions (i.e., resonant elements tuned together in afrequency range of +/−0.40), each pass band 38 illustrated in FIGS. 23(a)-23(c) would cover 33% of the normalized frequency range from −1.20 to1.20.

While the pass band 38 is illustrated in FIGS. 23( a)-23(c) as beingcentered within the sub-bands 36, the reflection zeroes 34 can bedisplaced within the stop band 32 (i.e., by adjusting the values of thenon-resonant elements) to selectively move the pass band 38 within aselected sub-band 36. In this case, the pass band 38 can be hoppedbetween sub-bands 36, as well as moved within each sub-band 36, therebydecreasing the amount the transmission zeroes 30 need to be adjusted forthe pass band 38 to cover the continuum of the desired frequency range.For example, FIG. 25 graphically shows the changes (and non-changes) inthe values for the non-resonant elements 22 as the pass band 38 is movedwithin the continuum of the nominal frequency range of −1.0 to 1.0.

Notably, the coupling values set forth in FIG. 25 are entirely differentfrom the coupling values set forth in FIG. 24, and therefore, it shouldbe appreciated that more than one coupling matrix exists for each filter(i.e., the coupling matrix does not have a unique solution). Forexample, FIG. 26 graphically shows another set of changes (andnon-changes) in the values for the non-resonant elements 22 as the passband 38 is moved within the continuum of the nominal frequency range of−1.0 to 1.0.

Selecting the ideal coupling matrix from the family of coupling matricesthat realize the same lossless filter function may be driven by furtheranalysis of the filter performance characteristics, such as powerhandling, intermodulation, or insertion loss. As demonstrated inco-pending patent application Ser. No. 12/163,837 (now U.S. Pat. No.7,924,114), entitled “Electrical Filters with Improved IntermodulationDistortion,” which is expressly incorporated herein by reference, smallchanges to the internal structure of the filter can produce enhancementof the filter's terminal performance characteristics without changingthe lossless filter function. The techniques disclosed in U.S. patentapplication Ser. No. 12/163,837, including changing the order oftransmission zeroes, can be applied to the filter circuits disclosed inthis application.

For example, the order in which the resonant elements 18 are disposedalong the signal transmission path 12 can be changed to create aplurality of filter solutions, a performance parameter (e.g.,intermodulation distortion) for each of the filter solutions can becomputed, the performance parameter can be compared for each of thefilter solutions, and one of the filter solutions can be selected basedon the comparison of the computed performance parameters. A couplingmatrix representation, such as that illustrated in FIG. 22, can begenerated for each of the filter solutions, in which case, theperformance parameter for each of the filter solutions can be computedfrom the respective coupling matrix representation. To confirm that thedifferent orders of resonant elements 18 used will produce uniquesolutions, the corresponding coupling matrices generated for thedifferent resonant element orders can be reduced down to their simplestform.

As briefly described above, the filter 10 can be tuned using a parameterextraction and analysis technique, and then varying one of thenon-resonant elements 22 to selectively displace the pass band 38 withinthe selected sub-band 36. In particular, the filter 10 may be operatedat an expected operating temperature to determine various initial orpre-tuning performance characteristics. For example, an HTS filter maybe operated at 77 degrees K and measurements taken. Parameter extractionmay then be performed by, for example, a network analyzer. For example,the measured S-parameter response (e.g., return loss) may be used todetermine various parameters (e.g., the resonator frequencies and/orresonator-to-resonator coupling values) associated with the filter.Next, the filter response may be optimized by, for example, a computer.Then, a difference between the extracted filter characteristics and theoptimized filter characteristics may be determined and used to provide atuning recipe. The filter may then be tuned according to the tuningrecipe. In various embodiments, this tuning may be done by, for example,selecting the capacitors that are switched on or off to adjust the passband 38 within a selected sub-band 36 using the electrical controller24. Once the filter has been tuned, it may be checked. For example, thefilter may again be operated at its operating temperature and measuredto determine the filter's new performance characteristics. If the newtuned performance characteristics, such as the frequency response and/orS-parameter response are acceptable, the filter may be packaged foroperation.

Another tuning technique for high-performance planar filters involvesusing one or more tuning elements that enable filter tuning. Forexample, and with reference to FIG. 27, tuning elements in the form oftuning forks 40, 42 can be disposed on the same substrate 44 as resonantelement 18, which in the illustrated case, takes the form of aspiral-in-spiral-out (SISO) shape half-wavelength structure. For thepurposes of illustration, only one resonant element 18 is illustrated inFIG. 27, although a complete filter may include multiple resonantelements 18, as illustrated in FIG. 1. In a multi-resonator planarfilter, each resonant element 18 may have tuning forks 40, 42. Portionsof the tuning forks 40, 42 may be removed from the substrate 44, e.g.,by scribing, to modify the frequency of the resonant element 18 to whichit is coupled, thereby displaying the transmission zero corresponding tothe frequency of the resonant element 18 along the stop band 32 relativeto the reflection zero(es) 34. In the case of turning multiple resonantelements 18, the frequencies of the resonant elements 18 can be modifiedto simultaneously displace the stop band 32 with the pass band 38 alonga frequency range. The tuning forks 40, 42 are capacitively coupled toone end of the resonant element 18 through a series inter-digitatedcapacitor 46.

Alternatively, the tuning forks 40, 42 may be directly coupled to theresonant element 18. However, the series capacitor can be designed toreduce the tuning sensitivity to approximately 10% of what would be seenif the tuning fork was directly connected to the resonator. This reducedsensitivity enables tuning by hand, e.g., with a mechanical device, suchas a diamond scribe pen. The hand scribing may be performed with adiamond scribe pen under a microscope. Alternate means of scribing thetuning forks 40, 42, such as a laser scribing tool, focused ion beams,or photolithography, may also be employed. In any case, the resonator 18may be tuned by physically disconnecting (e.g., scribing) part of thetuning forks 40, 42 in order to alter the capacitance of the filtercircuit.

For accuracy and ease of tuning, the tuning forks 40, 42 mayrespectively include a coarse scale 48 and a fine scale 50 to provideease of scribing for coarse and fine tuning. The scales 48, 50 may berelated to a tuning recipe. Although two tuning forks 40, 42 areillustrated, any number of tuning forks may be used depending on thedesired tuning range and tuning resolution.

A parameter extraction based technique may be used to diagnose thefilter couplings and resonant frequencies, and to provide a recipe forscribing the tuning forks. As such, a filter design is provided thatrealizes very accurate tuning without requiring any expensive tools.

As another example, tuning elements in the form of trimming tabs 52 canbe disposed on the same substrate 44 as the resonant element 18, asillustrated in FIG. 28. The trimming tabs 52 on located a resonator edgethat may be, for example, trimmed (i.e. disconnected from the circuit)to reduce the shunt capacitance of the resonant element 18. The trimmingtabs 52 may have discrete values that shift a resonant frequency of thefilter by different known amounts, and the amounts may be configured ina binary progression.

For example, the filter may have four trimming tabs 52 on each resonantelement 18 that can shift the resonant frequency in a binaryprogression, such as 1500 KHz, 800 KHz, 400 KHz, 200 kHz, and 100 KHz.In the illustrated embodiment, seven trimming tabs 52 of varying sizesare provided. In particular, the trimming tab 52(1) results in a 1500KHz frequency shift to the resonant element 18 when trimmed; thetrimming tab 52(2) results in an 800 KHz frequency shift to the resonantelement 18 when trimmed; the trimming tab 52(3) results in a 400 KHzfrequency shift to the resonant element 18 when trimmed; the trimmingtab 52(4) results in an 200 KHz frequency shift to the resonant element18 when trimmed; and each of the trimming tabs 52(5)-56(7) results in a100 KHz frequency shift to the resonant element 18 when trimmed. Thus,as an example, if the resonant element 18 needs a 670 KHz frequencyshift according to a tuning recipe, then the trimming tab 52(2) (400KHz), the trimming tab 52(3) (200 KHz), and one of the trimming tabs52(5)-56(7) may be removed from the substrate 44.

Further details discussing the use of tuning forks and trimming tabs totune resonators are described in U.S. patent application Ser. No.12/330,510, entitled “Systems and Methods for Tuning Filters,” which isexpressly incorporated herein by reference.

A parameter extraction based technique may be used to diagnose thefilter couplings and resonant frequencies, and to provide a recipeindicating which of the trimming tabs 52 should be disconnected ortrimmed from the resonator edges so as to produce a properly tunedfilter.

Referring now to FIG. 29, another tunable RF filter 100 constructed inaccordance with the present inventions will now be described. The RFfilter 100 is capable of being dynamically tuned to compensate forchanges in the operating temperature, which may otherwise cause the passband 38 to inadvertently move within the frequency range away from itsnominal as-designed position in a manner similar to the shifting of thepass band 78 shown in FIG. 11. That is, changes in operating temperaturecause the coupling values of the resonant elements 18 and non-resonantelements 22 to change from their nominal values (i.e., the reactances ofthe elements at the operating temperature at which the RF filter 100 isinitially tuned). For example, the reactances of the non-resonantelements 22 may change by ±1% for each 10° change in the operatingtemperature. Accordingly, the RF filter 100 can dynamically adjust thereactances of the resonant elements 18 and non-resonant elements 22 toreturn the pass band 38 to its nominal position within the frequencyrange.

The RF filter 100 is similar to the RF filter 10 illustrated in FIG. 13(a), with the exception that the RF filter 100 additionally includes anelectrical controller 124, a temperature sensor 126, and memory 128.Like the electrical controller 24 illustrated in FIG. 1, the electricalcontroller 124 is configured for adjusting the non-resonant elements 22to introduce and displace reflection zeroes along the stop band 32 tomove a narrow pass band 38 within the desired frequency range, and mayalso further adjust the frequencies of the resonant elements 18 viatuning elements (not shown) to move the transmission zeroes along thefrequency range to optimize the filter response. Unlike the electricalcontroller 24, the electrical controller 124 is configured fordynamically adjusting the resonant elements 18 and non-resonant elements22 to compensate for changes in the operating temperature.

To this end, the electrical controller 124 obtains a current operatingtemperature measurement from the temperature sensor 126, accesses alook-up table from memory 128, and adjusts the resonant elements 18 andnon-resonant elements 22 based on the look-up table. In particular, thelook-up table contains a plurality of reference operating temperatures,which may, e.g., range from −20° K to 100° K in increments of 10°, andfor each reference operating temperature, a corresponding set ofadjustment settings. Each adjustment setting controls the reactance ofone of the resonant elements 18 or one of the non-resonant elements 22.A typical set of adjustment settings will include adjustment settingsthat control a multitude of resonant elements 18 and non-resonantelements 22.

The electrical controller 124 applies the adjustment settings to theresonant elements 18 and non-resonant elements 22 via electrical signalsto adjust their respective reactances in a manner that returns the passband 38 to its nominal location within the frequency range. Inparticular, the electrical controller 124 compares the measuredoperating temperature to the reference operating temperatures in thelook-up table, selects the set of adjustment settings corresponding tothe reference operating temperature that best matches the measuredoperating temperature, and adjusts the reactances of the resonantelements 18 and non-resonant elements 22 in accordance with the selectedset of adjustment settings.

In the preferred embodiment, similar to the tuning technique illustratedin FIGS. 5( a)-5(d), the resonant elements 18 are adjusted in a mannerthat returns the selected sub-band 36 to its nominal position within thefrequency range, and the non-resonant elements 22 are adjusted in amanner that returns the pass band 38 to its nominal position within theselected sub-band 36. Alternatively, the resonant elements 18 may beadjusted in a manner that does not return the sub-band 36 to its nominalposition within the frequency range, or may not be adjusted at all, inwhich case, the non-resonant elements 22 may be adjusted in a mannerthat does not return the pass band 38 to its nominal position within theselected sub-band 36. In any event, the pass band 38 will be returned toits nominal position within the frequency range.

The nature of the adjustment settings will depend upon the mechanismthat is used to adjust the reactances of the resonant elements 18 andnon-resonant elements 22. For example, if each of the resonant elements18 and non-resonant elements 22 comprises parallel capacitors withswitches to form a variable capacitive circuit, each adjustment settingcan include data indicating which of the capacitors are switched on toinclude the respective capacitor within the capacitive circuit orswitched off to exclude the respective capacitor of the circuit, withthe goal of varying the reactance of the respective resonant element 18or non-resonant element 22 in a manner that locates the pass band 38 toits nominal position within the frequency range, or at least as near toits nominal position within the frequency range as possible given theresolution of the look-up table. Thus, in this case, for each measuredoperating temperature, the look-up table will have a set of on-offstates of the switched capacitors for each resonant elements 18 andnon-resonant element 22. The adjustment settings in the look-up tablecan be determined by exposing the filter 100 at each of the referenceoperating temperatures and using the afore-described parameterextraction and analysis technique to determine the adjustment settingsfor the resonant elements 18 and non-resonant elements 22.

Notably, the parallel capacitors that are turned on and off tocompensate for changes in operating temperature for the non-resonantelements 18 may include at least some of the parallel capacitors used tomove the pass band 38 between different sub-bands 36, as illustrated inFIGS. 15( a)-15(c). Furthermore, although the look-up table has beendescribed as including adjustment settings for only one of the sub-bands36, the look-up table can include adjustment settings for more than oneof the sub-bands 36. In this case, the adjustment settings for theparticular sub-band 36 in which the pass band 38 is currently located inmay be used to move the pass band 38 to its nominal position within thefrequency range in response to a change in the operating temperature.

Although particular embodiments of the present invention have been shownand described, it should be understood that the above discussion is notintended to limit the present invention to these embodiments. It will beobvious to those skilled in the art that various changes andmodifications may be made without departing from the spirit and scope ofthe present invention. For example, the present invention hasapplications well beyond filters with a single input and output, andparticular embodiments of the present invention may be used to formduplexers, multiplexers, channelizers, reactive switches, etc., wherelow-loss selective circuits may be used. Thus, the present invention isintended to cover alternatives, modifications, and equivalents that mayfall within the spirit and scope of the present invention as defined bythe claims.

What is claimed is:
 1. A method of constructing a radio frequency (RF)filter, comprising: designing a radio frequency (RF) filter thatincludes a signal transmission path having an input and an output, aplurality of resonant elements disposed along the signal transmissionpath between the input and the output, a plurality of non-resonantelements coupling the resonant elements together to form a stop bandhaving a plurality of transmission zeroes corresponding to respectivefrequencies of the resonant elements, and at least one sub-band betweenthe transmission zeroes, wherein the non-resonant elements comprise atleast one variable non-resonant element for selectively introducing atleast one reflection zero within the stop band to create a pass band inone of the at least one sub-bands; changing the order in which theresonant elements are disposed along the signal transmission path tocreate a plurality of filter solutions; computing a performanceparameter for each of the filter solutions; comparing the performanceparameters to each other; selecting one of the filter solutions based onthe comparison of the computed performance parameters; and constructingthe RF filter using the selected filter solution.
 2. The method of claim1, further comprising generating a coupling matrix representation foreach of the filter solutions, wherein the performance parameter for eachof the filter solutions is computed from the respective coupling matrixrepresentation.
 3. The method of claim 2, wherein the filter designincludes nodes respectively between the first set of non-resonantelements, nodes respectively between the plurality of resonant elementsand the second set of non-resonant elements, and nodes at the input andoutput, wherein each dimension of the coupling matrix includes thenodes.
 4. The method of claim 3, further comprising reducing eachcoupling matrix to its simplest form, and determining whether thereduced coupling matrices are different relative to each other.
 5. Themethod of claim 1, wherein the performance parameter is one or more ofan intermodulation distortion, insertion loss, and power handling. 6.The method of claim 1, wherein the at least one sub-band comprises aplurality of sub-bands.
 7. The method of claim 6, wherein the at leastone variable non-resonant element is for displacing the at least onereflection zero along the stop band to create the pass band withinselected ones of the sub-bands.
 8. The method of claim 7, wherein thepass band has substantially different bandwidths within the selectedsub-bands.
 9. The method of claim 6, wherein the at least one variablenon-resonant element is for displacing at least another reflection zerowithin the stop band to create another pass band within another one ofthe sub-bands.
 10. The method of claim 1, wherein the at least onevariable non-resonant element is for displacing the at least onereflection zero along the stop band to selectively move the pass bandwithin the one sub-band.
 11. The method of claim 1, wherein the at leastone reflection zero comprises a plurality of reflection zeroes.
 12. Themethod of claim 1, wherein the at least one variable non-resonantelement comprises a plurality of variable non-resonant elements.
 13. Themethod of claim 1, wherein the RF filter has at least one tuning elementconfigured for modifying the frequency of at least one of the resonantelements.
 14. The method of claim 1, wherein the at least one variablenon-resonant element has an adjustable susceptance.
 15. The method ofclaim 1, wherein the at least one variable non-resonant elementcomprises at least one of a variable capacitor, a loss-loss switch, avaractor, and a switched capacitor.
 16. The method of claim 1, whereineach of the resonant elements comprises a thin-film lumped elementstructure.
 17. The method of claim 16, wherein the thin-film lumpedelement structure comprises a high temperature superconductor (HTS). 18.The method of claim 1, wherein each of the resonant elements is anacoustic resonator.
 19. The method of claim 1, wherein the RF filterfurther includes a controller configured for generating electricalsignals to adjust the at least one variable non-resonant element. 20.The method of claim 1, wherein the number of the plurality of resonantelements is at least four.
 21. A method of constructing a radiofrequency (RF) filter, comprising: designing a radio frequency (RF)filter that includes a signal transmission path having an input and anoutput, a plurality of resonant elements disposed along the signaltransmission path between the input and the output, a plurality ofnon-resonant elements coupling the resonant elements together to form astop band having a plurality of transmission zeroes corresponding torespective frequencies of the resonant elements, and at least onesub-band between the transmission zeroes, wherein the non-resonantelements comprise at least one non-resonant element that introduces atleast one reflection zero within the stop band to create a pass band inone of the at least one sub-bands; changing the order in which theresonant elements are disposed along the signal transmission path tocreate a plurality of filter solutions; computing a performanceparameter for each of the filter solutions; comparing the performanceparameters to each other; selecting one of the filter solutions based onthe comparison of the computed performance parameters; and constructingthe RF filter using the selected filter solution.
 22. The method ofclaim 21, further comprising generating a coupling matrix representationfor each of the filter solutions, wherein the performance parameter foreach of the filter solutions is computed from the respective couplingmatrix representation.
 23. The method of claim 22, wherein the filterdesign includes nodes respectively between the first set of non-resonantelements, nodes respectively between the plurality of resonant elementsand the second set of non-resonant elements, and nodes at the input andoutput, wherein each dimension of the coupling matrix includes thenodes.
 24. The method of claim 23, further comprising reducing eachcoupling matrix to its simplest form, and determining whether thereduced coupling matrices are different relative to each other.
 25. Themethod of claim 24, wherein the performance parameter is one or more ofan intermodulation distortion, insertion loss, and power handling. 26.The method of claim 22, wherein the at least one sub-band comprises aplurality of sub-bands.
 27. The method of claim 22, wherein the at leastone reflection zero comprises a plurality of reflection zeroes.
 28. Themethod of claim 22, wherein the at least one non-resonant elementcomprises a plurality of non-resonant elements.
 29. The method of claim22, wherein the RF filter has at least one tuning element configured formodifying the frequency of at least one of the resonant elements. 30.The method of claim 22, wherein the number of the plurality of resonantelements is at least four.